Q.

Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +ρ and ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region                    [2013]

1 The electrostatic field is zero  
2 The electrostatic potential is constant  
3 The electrostatic field is constant in magnitude  
4 The electrostatic field has the same direction   

Ans.

(3, 4)

Electrostatic field at P is

EP=E1+E2=ρ3ε0C1P+(-ρ)3ε0C2P

=ρ3ε0(C1P-C2P)=ρ3ε0(C1P+PC2)=ρ3ε0(C1C2)